I find that the base Gaia Map is doing well with trails. Many trails of interest are on this map, both in the US and out of it. The "create a route" function works very well on trails. It is smoother than some of the other mapping sites, and currently my preference for long hike planning.

That said, of course not all trails are on this. OpenHikingMap layer is another option, but the standard Gaia layer tends to be better in my experience. The trails I find missing are usually pretty small, abandoned, etc.

To construct a trail route, just select the "create a route", then make it a walking route, then click away on the trail. I usually put in quite a few points, but the auto routing along the trails works well. If you find straight lines joining your points, try a being a little more precise with your point on the trail, or move it to a different location. But you really only need points to get the proper routing thru-out.